Preheat the oven to 400 degrees.
Melt the butter in a large saute pan or deep skillet over medium heat. Once its foam subsides, stir in the onion, carrots and a pinch of the salt. Cook for about 10 minutes, stirring a few times, until they have softened.
Sprinkle in the flour and stir to incorporate, then gradually pour in the milk while you are stirring, forming a sauce that is thickening. Then add the chicken bouillon base, peas, chicken pieces, dried thyme and a few grinds of pepper, stirring to blend well. Once the mixture begins to bubble at the edges, cook for 10 to 15 minutes. Taste and add salt and/or pepper, as needed.
Transfer this filling mixture to an 8-by-11-inch baking dish or casserole with a 3-quart capacity. Use the Tater Tots to cover the surface of the hotdish, arranging them snugly and neatly. Bake (middle rack) for about 30 minutes, or until golden brown.
Let cool slightly before serving.